Gary Taylor-Fletcher saw two long-range efforts cannon off the crossbar, while Charlie Adam hit the post with a first-half penalty.
The hosts did equalise early in the second half through Brett Ormerod's header, but their hard work was soon undone as Ian Evatt and Rob Edwards picked up straight red cards.
Ipswich capitalised on the dismissals, with substitute Owen Garvan firing home the winner from a free-kick with 13 minutes remaining.
Blackpool boss Ian Holloway named a strong side, with David Vaughan replacing Ben Burgess in the only change from the starting XI that defeated Derby 2-0 at Pride Park on Boxing Day.
Jon Walters and Stern John started in attack for Roy Keane's men, with Jon Stead missing through suspension.
The visitors made a stunning start to the game and took the lead when on-loan Sunderland midfielder Colback fired a shot into the top-right corner from the edge of the area.
Blackpool responded positively and Alex Baptiste almost levelled seven minutes later when he nodded over the bar from a Vaughan corner.
Town goalkeeper Arran Lee-Barrett was then called upon to keep out a headed effort from Jason Euell, while at the other end John volleyed wide from Liam Rosenior's cross.
Rosenior was the next to try his luck in a frenetic opening and Seasiders keeper Paul Rachubka had to make a fine save to keep out the full-back's long-range strike.
As chances continued to come at either end, Blackpool's Taylor-Fletcher saw a 25-yard effort strike the crossbar.
The hosts had an even better opportunity to pull level in the 24th minute, but Adam struck the post with his penalty after Lee-Barrett had brought down Ormerod in the box.
Incredibly, the hosts were denied by the woodwork for a third time two minutes before the interval as Taylor-Fletcher fired against the bar for a second time.
But they finally pulled level five minutes into the second half as Ormerod met Adam's left-wing cross with a powerful header that flew into the roof of the net.
Blackpool's joy was short-lived as Evatt was dismissed in the 55th minute for hauling down Colback as the youngster burst clear.
And although the hosts continued to battle away, they suffered another blow with 15 minutes remaining as Edwards - who had replaced Vaughan on the hour mark - also saw red for a foul on Walters.
Garvan fired home the resulting free-kick to put Ipswich back in front and substitute Connor Wickham twice went close to extending the lead in the closing stages as the visitors made the most of their numerical advantage.